<PAGE>
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                            ------------------------

                                   FORM 10-Q

[X] QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE QUARTERLY PERIOD ENDED MARCH 31, 1999

                                       OR

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
   ACT OF 1934 FOR THE TRANSITION PERIOD FROM _______________ TO _______________

                         COMMISSION FILE NUMBER: 0-6910

                            ------------------------

                               TEL OFFSHORE TRUST
             (Exact Name of Registrant as Specified in its Charter)

                 TEXAS                                           76-6004064
        (State of Incorporation,                              (I.R.S. Employer
            or Organization)                                 Identification No.)

          CHASE BANK OF TEXAS,
          NATIONAL ASSOCIATION
        CORPORATE TRUST DIVISION
            712 MAIN STREET
             HOUSTON, TEXAS                                         77002
         (Address of Principal                                   (Zip Code)
           Executive Offices)

       Registrant's Telephone Number, Including Area Code: (713) 216-5712

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days.  Yes [X]  No [ ]

     Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

     As of May 7, 1999 -- 4,751,510 Units of Beneficial Interest in TEL Offshore
Trust.

================================================================================
<PAGE>
                   NOTE REGARDING FORWARD-LOOKING STATEMENTS

     This Form 10-Q includes "forward-looking statements" within the meaning
of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities Exchange Act of 1934, as amended. All statements other than
statements of historical facts included in this Form 10-Q are forward-looking
statements. Although the Working Interest Owners (as defined herein) have
advised the Trust that they believe that the expectations reflected in the
forward-looking statements contained herein are reasonable, no assurance can be
given that such expectations will prove to have been correct. Important factors
that could cause actual results to differ materially from expectations
("Cautionary Statements") are disclosed in this Form 10-Q, including without
limitation in conjunction with the forward-looking statements included in this
Form 10-Q. All subsequent written and oral forward-looking statements
attributable to the Trust or persons acting on its behalf are expressly
qualified in their entirety by the Cautionary Statements.

                                       i

<PAGE>
                        PART I -- FINANCIAL INFORMATION

ITEM 1 -- FINANCIAL STATEMENTS

               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

<TABLE>
<CAPTION>
                                        MARCH 31,       DECEMBER 31,
                                           1999             1998
                                        ----------      ------------
<S>                                     <C>             <C>
                                        (UNAUDITED)
ASSETS
Cash and cash equivalents............   $1,439,836       $3,077,569
Net overriding royalty interest in
  producing oil and gas properties,
  net of accumulated amortization of
  $27,828,766 and $27,825,034, 
  respectively.......................      438,889          442,621
                                        ----------      ------------
Total assets.........................   $1,878,725       $3,520,190
                                        ==========      ============
LIABILITIES AND TRUST CORPUS
Distribution payable to Unit
  holders............................   $   55,593       $1,711,534
Reserve for future Trust expenses....    1,384,243        1,366,035
Commitments and contingencies (Note
  7).................................
Trust corpus (4,751,510 Units of
  beneficial interest authorized and
  outstanding).......................      438,889          442,621
                                        ----------      ------------
Total liabilities and Trust corpus...   $1,878,725       $3,520,190
                                        ==========      ============
</TABLE>

                       STATEMENTS OF DISTRIBUTABLE INCOME
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                           THREE MONTHS ENDED
                                               MARCH 31,
                                       --------------------------
                                           1999          1998
                                       ------------  ------------
<S>                                    <C>           <C>
Royalty income.......................  $     88,696  $  1,934,392
Interest income......................        15,832        18,702
                                       ------------  ------------
                                            104,528     1,953,094
Decrease (increase) in reserve for
  future Trust expenses..............       (18,208)      106,654
General and administrative
  expenses...........................       (30,727)      (95,370)
                                       ------------  ------------
Distributable income.................  $     55,593  $  1,964,378
                                       ============  ============
Distributions per Unit (4,751,510
  Units).............................  $    .011700  $    .413421
                                       ============  ============
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       1
<PAGE>
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                           THREE MONTHS ENDED
                                               MARCH 31,
                                       --------------------------
                                           1999          1998
                                       ------------  ------------
<S>                                    <C>           <C>
Trust corpus, beginning of period....  $    442,621  $    703,214
Distributable income.................        55,593     1,964,378
Distribution payable to Unit
  holders............................       (55,593)   (1,964,378)
Amortization of net overriding
  royalty interest...................        (3,732)      (63,678)
                                       ------------  ------------
Trust corpus, end of period..........  $    438,889  $    639,536
                                       ============  ============
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       2
<PAGE>
                               TEL OFFSHORE TRUST
                         NOTES TO FINANCIAL STATEMENTS
                                  (UNAUDITED)

NOTE 1 -- TRUST ORGANIZATION

     Tenneco Offshore Company, Inc. ("Tenneco Offshore") created the TEL
Offshore Trust ("Trust") effective January 1, 1983, pursuant to the Plan of
Dissolution ("Plan") approved by Tenneco Offshore's stockholders on December
22, 1982. In accordance with the Plan, the TEL Offshore Trust Partnership
("Partnership") was formed in which the Trust owns a 99.99% interest and
Tenneco Oil Company ("Tenneco") initially owned a .01% interest. In general,
the Plan was effected by transferring an overriding royalty interest
("Royalty") equivalent to a 25% net profits interest in the oil and gas
properties (the "Royalty Properties") of Tenneco Exploration, Ltd.
("Exploration I") located offshore Louisiana to the Partnership and issuing
certificates evidencing units of beneficial interest in the Trust ("Units") in
liquidation and cancellation of Tenneco Offshore's common stock.

     On October 31, 1986, Exploration I was dissolved and the oil and gas
properties of Exploration I were distributed to Tenneco subject to the Royalty.
Tenneco, who was then serving as the Managing General Partner of the
Partnership, assumed the obligations of Exploration I, including its obligations
under the instrument conveying the Royalty to the Partnership (the
"Conveyance"). The dissolution of Exploration I had no impact on future cash
distributions to Unit holders.

     On November 18, 1988, Chevron U.S.A. Inc. ("Chevron") acquired most of
the Gulf of Mexico offshore oil and gas properties of Tenneco, including all the
Royalty Properties. As a result of the acquisition, Chevron replaced Tenneco as
the Working Interest Owner and Managing General Partner of the Partnership.
Chevron also assumed Tenneco's obligations under the Conveyance.

     On October 30, 1992, PennzEnergy Company ("PennzEnergy") acquired certain
oil and gas producing properties from Chevron, including four of the Royalty
Properties. The four Royalty Properties acquired by PennzEnergy were East
Cameron 354, Eugene Island 348, Eugene Island 367 and Eugene Island 208. As a
result of such acquisition, PennzEnergy replaced Chevron as the Working Interest
Owner of such properties on October 30, 1992. PennzEnergy also assumed Chevron's
obligations under the Conveyance with respect to such properties.

     On December 1, 1994, Texaco Exploration and Production Inc. ("Texaco")
acquired two of the Royalty Properties from Chevron. The Royalty Properties
acquired by Texaco were West Cameron 643 and East Cameron 371/381. As a result
of such acquisitions, Texaco replaced Chevron as the Working Interest Owner of
such properties on December 1, 1994. Texaco also assumed Chevron's obligations
under the Conveyance with respect to such properties.

     On October 1, 1995, SONAT Exploration Company ("SONAT") acquired the East
Cameron 354 property from PennzEnergy. In addition, on October 1, 1995, Amoco
Production Company ("Amoco") acquired the Eugene Island 367 property from
PennzEnergy. As a result of such acquisitions, SONAT and Amoco replaced
PennzEnergy as the Working Interest Owners of the East Cameron 354 and Eugene
Island 367 properties, respectively, on October 1, 1995 and also assumed
PennzEnergy's obligations under the Conveyance with respect to such properties.

     Effective January 1, 1998, Energy Resource Technology, Inc. ("Energy")
acquired the East Cameron 354 property from SONAT. As a result of such
acquisition, Energy replaced SONAT as the Working Interest Owner of the East
Cameron 354 property effective January 1, 1998, and also assumed SONAT's
obligations under the Conveyance with respect to such property. In October 1998,
Amerada Hess Corporation ("Amerada") acquired the East Cameron 354 property
from Energy effective January 1, 1998. As a result of such acquisition, Amerada
replaced Energy as the Working Interest Owner of the East

                                       3
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

Cameron 354 property effective January 1, 1998, and also assumed Energy's
obligations under the Conveyance with respect to such property.

     All of the Royalty Properties continue to be subject to the Royalty, and it
is anticipated that the Trust and the Partnership, in general, will continue to
operate as if the above-described sales of the Royalty Properties had not
occurred.

     Unless the context in which such terms are used indicates otherwise, in
these Notes the terms "Working Interest Owner" and "Working Interest Owners"
generally refer to the owner or owners of the Royalty Properties (Exploration I
through October 31, 1986; Tenneco for periods from October 31, 1986 until
November 18, 1988; Chevron with respect to all Royalty Properties for periods
from November 18, 1988 until October 30, 1992, and with respect to all Royalty
Properties except East Cameron 354, Eugene Island 348, Eugene Island 367 and
Eugene Island 208 for periods from October 30, 1992 until December 1, 1994, and
with respect to the same properties except West Cameron 643 and East Cameron
371/381 thereafter; PennzEnergy with respect to East Cameron 354, Eugene Island
348, Eugene Island 367 and Eugene Island 208 for periods from October 30, 1992
until October 1, 1995, and with respect to Eugene Island 348 and Eugene Island
208 thereafter; Texaco with respect to West Cameron 643 and East Cameron 371/381
for periods beginning on or after December 1, 1994; SONAT with respect to East
Cameron 354 for periods beginning on or after October 1, 1995; and Amoco with
respect to Eugene Island 367 for periods beginning on or after October 1, 1995;
and Amerada with respect to East Cameron 354 for periods beginning on or after
January 1, 1998).

NOTE 2 -- BASIS OF ACCOUNTING

     The accompanying unaudited financial information has been prepared by Chase
Bank of Texas, National Association ("Corporate Trustee") in accordance with
the instructions to Form 10-Q and does not include all of the information
required by generally accepted accounting principles for complete financial
statements, although the Corporate Trustee and the individual trustees
(collectively, the "Trustees") believe that the disclosures are adequate to
make the information presented not misleading. The information furnished
reflects all adjustments which are, in the opinion of the Trustees, necessary
for a fair presentation of the results for the interim periods presented. The
financial information should be read in conjunction with the financial
statements and notes thereto included in the Trust's Annual Report on Form 10-K
for the year ended December 31, 1998.

     The financial statements of the Trust are prepared on the following basis:

          (a)  Royalty income is recorded when received by the Corporate Trustee
               on the last business day of each calendar quarter; and

          (b)  Trust general and administrative expenses are recorded when paid,
               except for the cash reserved for future general and
               administrative expenses, as discussed in Note 6.

     This manner of reporting income and expenses is considered to be the most
meaningful because the quarterly distributions to Unit holders are based on net
cash receipts received from the Working Interest Owners. The financial
statements of the Trust differ from financial statements prepared in accordance
with generally accepted accounting principles, because, under such principles,
Royalty income and Trust general and administrative expenses for a quarter would
be recognized on an accrual basis. In addition, amortization of the overriding
royalty interest, which is calculated on a units-of-production basis, is charged
directly to Trust corpus since such amount does not affect distributable income.

                                       4
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

     Cash and cash equivalents include all highly liquid, short-term investments
with original maturities of three months or less.

NOTE 3 -- OVERRIDING ROYALTY INTEREST

     The Royalty entitles the Trust to its share (99.99%) of 25% of the Net
Proceeds attributable to the Royalty Properties. The Conveyance, dated January
1, 1983, provides that the Working Interest Owners will calculate, for each
period of three months commencing the first day of February, May, August and
November, an amount equal to 25% of the Net Proceeds from their oil and gas
properties for the period. Generally, Net Proceeds are the amounts received by
the Working Interest Owners from the sale of minerals from the Royalty
Properties less operating and capital costs incurred, management fees and
expense reimbursements owing to the Managing General Partner of the Partnership,
applicable taxes other than income taxes, and a special cost reserve. The
Special Cost Reserve Account is established for the future costs to be incurred
to plug and abandon wells, dismantle and remove platforms, pipelines and other
production facilities, and for the estimated amount of future capital
expenditures on the Royalty Properties. Net Proceeds do not include amounts
received by the Working Interest Owners as advance gas payments, "take-or-pay"
payments or similar payments unless and until such payments are extinguished or
repaid through the future delivery of gas.

NOTE 4 -- DISTRIBUTIONS TO UNIT HOLDERS

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. The
amounts distributed are determined on a quarterly basis and are payable to Unit
holders of record as of the last business day of each calendar quarter. However,
cash distributions are made in January, April, July and October and include
interest earned from the quarterly record date to the date of distribution.

NOTE 5 -- SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for the reserve of funds for estimated future
"Special Costs" of plugging and abandoning wells, dismantling platforms and
other costs of abandoning the Royalty Properties, as well as for the estimated
amount of future drilling projects and other capital expenditures on the Royal
Properties. As provided in the Conveyance, the amount of funds to be reserved is
determined based on certain factors, including estimates of aggregate future
production costs, aggregate future Special Costs, aggregate future net revenues
and actual current net proceeds. Deposits into this account reduce current
distributions and are placed in an escrow account and invested in short-term
certificates of deposit. Such account is herein referred to as the "Special
Cost Escrow Account." The Trust's share of interest generated from the Special
Cost Escrow Account serves to reduce the Trust's share of allocated production
costs. Special Cost Escrow funds will generally be utilized to pay Special Costs
to the extent there are not adequate current net proceeds to pay such costs.
Special Costs that have been paid are no longer included in the Special Cost
Escrow calculation. Deposits to the Special Cost Escrow Account will generally
be made when the balance in the Special Cost Escrow Account is less than 125% of
future Special Costs and there is a Net Revenues Shortfall (a calculation of the
excess of estimated future costs over estimated future net revenues pursuant to
a formula contained in the Conveyance). When there is not a Net Revenues
Shortfall, amounts in the Special Cost Escrow Account will generally be
released, to the extent that Special Costs have been incurred. Amounts in the
Special Cost Escrow Account generally will also be released when the balance in
such account exceeds 125% of future Special Costs. In the first quarter of 1998,
there was a net

                                       5
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

release of funds from the Special Cost Escrow Account. The Trust's share of the
funds released was approximately $513,800. The release was primarily a result of
a decrease in the current estimate of projected capital expenditures, production
costs and abandonment costs of the Royalty Properties. In the first quarter of
1999, there was a net deposit of funds into the Special Cost Escrow Account. The
Trust's share of the funds deposited was approximately $461,000. The deposit was
primarily a result of an increase in the current estimate of projected capital
expenditures of the Royalty Properties. As of March 31, 1999, approximately
$3,790,000 remained in the Special Cost Escrow Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production costs, other abandonment
costs, other capital expenditures and changes in the estimates and factors
described above. Such deposits could result in a significant reduction in
Royalty income in the periods in which such deposits are made, including the
possibility that no Royalty income would be received in such periods.

NOTE 6 -- EXPENSE RESERVE

     At December 31, 1991, a cash reserve of $120,000 had been established for
future Trust general and administrative expenses. During 1992 and 1993, in
anticipation of future periods when the cash received from the Royalty may not
be sufficient for payment of Trust expenses, the reserve for future Trust
general and administrative expenses was increased each quarter by an amount
equal to the difference between $150,000 and the amount of the Trust's general
and administrative expenses for such quarter. In 1994, in anticipation of future
periods when the cash received from the Royalty may not be sufficient for
payment of Trust expenses, the Trust determined, in accordance with the Trust
Agreement, to begin further increasing the Trust's cash reserve each quarter by
an amount equal to the difference between $200,000 and the amount of the Trust's
general and administrative expenses for such quarter. During 1994 and 1995, the
aggregate amount of cash reserved by the Trust was $347,638 and $370,258,
respectively. During 1996, the Trust used $397,845 from the Trust's cash reserve
account to pay the Trust's general and administrative expenses for the first,
second and fourth quarters, when no royalty income was received by the Trust. In
the third quarter of 1996, when Royalty income was received, the Trust reserved
$99,536. Therefore, the net cash used from the Trust's cash reserve account in
1996 was $298,309. During 1997, the aggregate amount of cash reserved by the
Trust was $593,066. In the first quarter of 1998, the Trust determined that the
Trust's cash reserve was currently sufficient to provide for future
administrative expenses in connection with the winding up of the Trust. The
Trust determined that a cash reserve equal to three times the average expenses
of the Trust during each of the past three years was sufficient at this time to
provide for future administrative expenses in connection with the winding up of
the Trust. This reserve amount for 1998 was $1,366,035. The excess amount of
$106,654 was distributed to Unit holders in the first quarter of 1998, and no
deposits were made to the Trust's cash reserve account during 1998. The reserve
amount for 1999 is $1,384,243. A deposit of $18,208 was made to the Trust's cash
reserve account in the first quarter of 1999.

NOTE 7 -- COMMITMENTS AND CONTINGENCIES

     During 1994, PennzEnergy, the Working Interest Owner on the Eugene Island
348 property, settled a gas imbalance on that property for approximately
$2,696,000. The Trust's share of this settlement amount was approximately
$674,000, of which approximately $387,300 has been recovered from the Trust by
PennzEnergy through the first quarter of 1999. The remainder will be subject to
recovery from the Trust in future periods, in accordance with the Conveyance.
PennzEnergy has advised the Trust that future Royalty income attributable to all
of the Royalty Properties owned by PennzEnergy will be used to offset the
Trust's

                                       6
<PAGE>
                               TEL OFFSHORE TRUST
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)

share of such settlement amounts. Based on current production, prices and
expenses for the Royalty Properties owned by PennzEnergy, it is estimated that
Royalty income attributable to such properties will be retained by PennzEnergy
for the remaining life of the Trust. The Trust does not anticipate that
retention of such Royalty income by PennzEnergy will have a material effect on
the Trust's Royalty income as a whole.

     During the first quarter of 1999, the Working Interest Owner of East
Cameron 371/381 informed the Trust that the Working Interest Owner overpaid
royalties to the Trust in the third and fourth quarters of 1998 in an amount
totaling $1,090,367. The Working Interest Owner of East Cameron 371/381 recouped
$404,190 of the overpayment from production in the first quarter of 1999 and
will recoup additional royalties of $686,177 in future periods through future
production on this property and West Cameron 643, which properties are operated
by this Working Interest Owner.

     The Working Interest Owners have advised the Trust that, although they
believe that they are in general compliance with applicable health, safety and
environmental laws and regulations that have taken effect at the federal, state
and local levels, costs may be incurred to comply with current and proposed
environmental legislation which could result in increased operating expenses on
the Royalty Properties.

                                       7

<PAGE>
ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS

FINANCIAL REVIEW

THREE MONTHS ENDED MARCH 31, 1999 AND 1998

     Distributions to Unit holders for the three months ended March 31, 1999
amounted to $55,593 or $.011700 per Unit as compared to $1,964,378 or $.413421
per Unit for the same period in 1998. The decrease in distributable income for
the first quarter of 1999 was primarily due to a deposit of $461,000 into the
Trust's Special Cost Escrow Account as compared to a net release of $513,800 in
the first quarter of 1998 and the $404,190 recoupment by the Working Interest
Owner of East Cameron 371/381 in the first quarter of 1999 as described below.

     During the first quarter of 1999, the Trust discovered that the Working
Interest Owner of East Cameron 371/381 had overpaid royalties to the Trust in
the third and fourth quarters of 1998 in an amount totaling $1,090,367. The
Working Interest Owner of East Cameron 371/381 recouped $404,190 of the
overpayment from production in the first quarter of 1999 and will recoup
additional royalties of $686,177 in future periods through future production on
this property and West Cameron 643, which properties are operated by this
Working Interest Owner. The following summary presents the first quarter of 1999
activity inclusive of this one-time adjustment.

     Gas revenues decreased approximately 134% in the first quarter of 1999
compared to the first quarter of 1998 primarily due to a 142% decrease in gas
volumes. This decrease in volumes was primarily attributable to the one-time
adjustment referred to above on the East Cameron 371/381 property. In addition,
there was a 23% decrease in the average price received for natural gas from
$2.75 per Mcf in the first quarter of 1998 to $2.11 per Mcf in the first quarter
of 1999. Crude oil and condensate revenues decreased approximately 57% in the
first quarter of 1999 in comparison to the same period in 1998 primarily due to
a 41% decrease in the average price received from $17.24 per barrel in the first
quarter of 1998 to $10.09 per barrel in the first quarter of 1999. In addition,
there was a 26% decrease in crude oil and condensate volumes from the 1998 first
quarter to the 1999 first quarter due primarily to the one-time adjustment
referred to above on the East Cameron 371/381 property. The Trust's share of
capital expenditures decreased approximately 73% or $577,183 in the first
quarter of 1999 as compared to the same period in 1998 primarily due to drilling
activity on the B-7, B-9 and B-12 wells on the Eugene Island 339 property in the
first quarter of 1998. The Trust's share of operating expenses increased by
approximately 122% or $137,721 in the first quarter of 1999 as compared to the
same period in 1998 due primarily to lower costs as a result of the removal of a
compressor from the West Cameron 643 property in the first quarter of 1998.

     For the first quarter of 1999, the Trust had undistributed net loss of
$667,545. Undistributed net loss represents negative Net Proceeds generated
during the respective period. An undistributed net loss is carried forward and
offset, in future periods, by positive Net Proceeds earned by the related
Working Interest Owner(s). Undistributed net income represents positive Net
Proceeds, generated during the respective period, that were applied to an
existing loss carryforward. The undistributed net loss for the first quarter of
1999 was primarily related to the one-time adjustment referred to above on the
East Cameron 371/381 property.

     In the first quarter of 1999, there was a deposit of funds into the Special
Cost Escrow Account. The Trust's share of the funds deposited was approximately
$461,000, compared to a release of funds from the Special Cost Escrow Account of
$513,800 net to the Trust in the first quarter of 1998. The Special Cost Escrow
is set aside for estimated abandonment costs and future capital expenditures as
provided for in the

                                       8
<PAGE>
Conveyance. For additional information relating to the Special Cost Escrow see
"Special Cost Escrow Account" below.

RESERVE FOR FUTURE TRUST EXPENSES

     In accordance with the provisions of the Trust Agreement, generally all Net
Proceeds received by the Trust, net of Trust general and administrative expenses
and any cash reserves established for the payment of contingent or future
obligations of the Trust, are distributed currently to the Unit holders. During
1992 and 1993, in anticipation of future periods when the cash received from the
Royalty may not be sufficient for payment of Trust expenses, the reserve for
future Trust general and administrative expenses was increased each quarter by
an amount equal to the difference between $150,000 and the amount of the Trust's
general and administrative expenses for such quarter. In 1994 in anticipation of
future periods when the cash received from the Royalty may not be sufficient for
payment of Trust expenses, the Trust determined, in accordance with the Trust
Agreement, to begin further increasing the Trust's cash reserve each quarter by
an amount equal to the difference between $200,000 and the amount of the Trust's
general and administrative expenses for such quarter. During 1994 and 1995, the
aggregate amount of cash reserved by the Trust was $347,638 and $370,258,
respectively. During 1996, the Trust used cash of $397,845 from the Trust's cash
reserve account to pay the Trust's general and administrative expenses due to
the absence of Royalty income during the first, second and fourth quarters. In
the third quarter of 1996, when Royalty income was received, the Trust reserved
$99,536. Therefore, the net cash used from the Trust's cash reserve account in
1996 was $298,309. During 1997, the aggregate amount of cash reserved by the
Trust was $593,066. In the first quarter of 1998, the Trust determined that the
Trust's cash reserve was currently sufficient to provide for future
administrative expenses in connection with the winding up of the Trust. The
Trust determined that a cash reserve equal to three times the average expenses
of the Trust during each of the past three years was sufficient at this time to
provide for future administrative expenses in connection with the winding up of
the Trust. This reserve amount for 1998 was $1,366,035. The excess amount of
$106,654 was distributed to Unit holders in the first quarter of 1998, and no
deposits were made to the Trust's cash reserve account during 1998. The reserve
amount for 1999 is $1,384,243. A deposit of $18,208 was made to the Trust's cash
reserve account in the first quarter of 1999.

OTHER

     The amount of cash distributed by the Trust is dependent on, among other
things, the sales prices and quantities of oil and gas produced from the Royalty
Properties. It should be noted that substantial uncertainties exist with regard
to future oil and gas prices, which are subject to material fluctuations due to
changes in production levels and pricing and other actions taken by major
petroleum producing nations, as well as the regional supply and demand for oil
and gas, weather, industrial growth, conservation measures, competition and
other variables.

OPERATIONAL REVIEW

THREE MONTHS ENDED MARCH 31, 1999 AND 1998

     VOLUMES AND DOLLAR AMOUNTS DISCUSSED BELOW REPRESENT AMOUNTS RECORDED BY
THE WORKING INTEREST OWNERS UNLESS OTHERWISE SPECIFIED.

     Ship Shoal 182/183 crude oil revenues decreased from $4,628,394 in the
first quarter of 1998 to $1,744,388 in the first quarter of 1999, primarily due
to a decrease in the average crude oil price from $17.67 per barrel in the first
quarter of 1998 to $10.61 per barrel for the same period in 1999. In addition,
there was a decrease in crude oil production from 261,918 barrels in the first
quarter of 1998 to 164,425 barrels in the first quarter of 1999. The decrease in
crude oil production was due primarily to the lower production in 1999 on the
B-11, B-12 and B-13 wells that were drilled in 1996 and the B-15 well that was

                                       9
<PAGE>
drilled in the third quarter of 1997. Gas revenues decreased from $883,244 in
the first quarter of 1998 to $531,939 in the first quarter of 1999 primarily due
to a decrease in the average natural gas sales price from $2.82 per Mcf in the
first quarter of 1998 to $1.94 per Mcf in the same period of 1999. In addition,
there was a decrease in gas volumes from 330,190 Mcf in the first quarter of
1998 to 284,721 Mcf in the first quarter of 1999. The decrease in gas volumes
was primarily due to the E-10 well watering out in the first quarter of 1999.
The gas from Ship Shoal 182/183 is committed to Dynegy Inc. ("Dynegy") at a
calculated price based on the monthly Inside FERC Tennesse-Louisiana Zone 1
Index. In addition, the Working Interest Owner has advised the Trust that
approximately 4,844 Mcf have been undertaken by the Working Interest Owner from
this property as of January 31, 1999. The Trust's share of this undertake
position is approximately 1,211 Mcf. Accordingly, gas revenues from this
property may be increased in future periods while overproduced parties repay
their share of the gas imbalance. Chevron has advised the Trust that sufficient
gas reserves exist on Ship Shoal 182/183 for underproduced parties to recoup
their share of the gas imbalance on this property. Capital expenditures
decreased from $196,876 in the first quarter of 1998 to $15,990 in the first
quarter of 1999. Operating expenses decreased from $425,308 in the first quarter
of 1998 to $358,283 for the same period in 1999 due to a reduction in drilling
activity. The Working Interest Owner has advised the Trust that it plans to
drill a horizontal well on this property during the second quarter of 1999 at an
approximate cost of $1.1 million ($275,000 net to the Trust).

     Eugene Island 339 crude oil revenues decreased from $1,161,849 in the first
quarter of 1998 to $973,740 for the same period in 1999 due primarily to a
decrease in the average crude oil price from $15.68 per barrel in the first
quarter of 1998 to $9.72 per barrel in the first quarter of 1999. The decrease
in the average crude oil price was partially offset by an increase in volumes
from 74,103 barrels in the first quarter of 1998 to 100,148 barrels in the first
quarter of 1999 due primarily to successful workovers on the B-4 and B-12 wells,
completed during the third quarter of 1998. Gas revenues decreased from $296,844
in the first quarter of 1998 to $184,691 in the first quarter of 1999 due to a
decrease in the average price received for natural gas from $2.84 per Mcf in the
first quarter of 1998 to $2.07 per Mcf for the same period in 1999. In addition,
there was a decrease in gas volumes from 110,702 Mcf in the first quarter of
1998 to 98,202 Mcf in the first quarter of 1999. The decrease in volumes was due
primarily to continued natural production decline. The Working Interest Owner
has advised the Trust that there is an overtake imbalance position of
approximately 24,127 Mcf on this property as of January 31, 1999. The Trust's
share of this overtake position is approximately 6,032 Mcf. Accordingly, gas
revenues from this property may be reduced in future periods while underproduced
parties recoup their share of the gas imbalance. Chevron has advised the Trust
that sufficient gas reserves exist on the Eugene Island 339 for underproduced
parties to recoup their share of the gas imbalance on this property. The gas
from this property is currently committed to Dynegy at a calculated price based
on the monthly Inside FERC Tennessee-Louisiana Zone 1 Index. Capital
expenditures decreased from $1,454,387 in the first quarter of 1998 to $576,865
in the first quarter of 1999 due primarily to drilling activity on the B-7, B-9
and B-12 wells in the first quarter of 1998. Operating expenses increased from
$138,407 in the first quarter of 1998 to $376,537 in the first quarter of 1999
due primarily to an adjustment to properly reflect capital costs in the first
quarter of 1998.

     West Cameron 643 gas revenues decreased from $1,990,085 in the first
quarter of 1998 to $1,284,949 in the first quarter of 1999 due primarily to a
decrease in the average price received for natural gas from $2.70 per Mcf in the
first quarter of 1998 to $2.00 per Mcf in the first quarter of 1999. In
addition, there was a decrease in gas volumes from 738,177 Mcf in the first
quarter of 1998 to 641,400 Mcf for the same period in 1999. The decrease in
volumes was due primarily to the B-9 well watering out in the first quarter of
1999. The Working Interest Owner has advised the Trust that the gas from this
property is currently committed under the contract with Texaco Natural Gas, Inc.
pursuant to an agreement for gas to be purchased at a price based on a weighted
average calculation using the Inside FERC's Gas Market Report first of month
indices for Columbia Gulf Transmission Co. -- Louisiana and Tennessee Gas
Pipeline --

                                       10
<PAGE>
Louisiana. Capital expenditures decreased from $158,090 in the first quarter of
1998 to $40,043 in the first quarter of 1999. Operating expenses increased
$310,697 in the first quarter of 1999 as compared to the same period in 1998.
This increase was the result of the absence of a compressor abandonment credit
of approximately $825,000 in 1998 which was partially offset by decreased
operating costs associated with the A-17 workover in 1999. The Working Interest
Owner has advised the Trust that it plans to perform three well workovers in
1999 on this property at an estimated cost of approximately $1.3 million
($325,000 net to the Trust).

     East Cameron 371/381 started production in May 1998. Gas revenues on this
property were $796,839 in the first quarter of 1999. Gas volumes were 362,647
Mcf and the average price received for natural gas was $2.20 per Mcf in the
first quarter of 1999. However, in 1998, the gas revenues and volumes included
overpaid revenues and volumes made by the Working Interest Owner of $4,272,556
and 2,071,162 Mcf, respectively. Therefore, the adjustment for this 1998
overpayment was made in the first quarter of 1999. Capital expenditures were
$193,656 in the first quarter of 1999. Operating expenses were $31,827 in the
first quarter of 1999. The Working Interest Owner has advised the Trust that the
A-5 well was drilled in November 1998 at a cost of approximately $1,000,000
($250,000 net to the Trust). In addition, there are plans to drill the A-6 well
in the third quarter of 1999 at an estimated cost of approximately $1.8 million
($450,000 net to the Trust).

FUTURE NET REVENUES AND TERMINATION OF THE TRUST

     Based on a reserve study provided to the Trust by DeGolyer and MacNaughton,
independent petroleum engineers, it was estimated that as of October 31, 1998
future net revenues attributable to the Trust's royalty interests approximated
$16.3 million. Such reserve study also indicates that approximately 79% of the
future net revenues from the Royalty Properties are expected to be received by
the Trust during the next three years. In addition, because the Trust will
terminate in the event estimated future net revenues fall below $2 million, it
would be possible for the Trust to terminate even though some or all of the
Royalty Properties continued to have remaining productive lives. Upon
termination of the Trust, the Trustees will sell for cash all of the assets held
in the Trust estate and make a final distribution to Unit holders of any funds
remaining after all Trust liabilities have been satisfied. The estimates of
future net revenues discussed above are subject to large variances from year to
year and should not be construed as exact. There are numerous uncertainties
present in estimating future net revenues for the Royalty Properties. The
estimate may vary depending on changes in market prices for crude oil and
natural gas, the recoverable reserves, annual production and costs assumed by
DeGolyer and MacNaughton. In addition, future economic and operating conditions
as well as results of future drilling plans may cause significant changes in
such estimate. The discussion set forth above is qualified in its entirety by
reference to the Trust's 1998 Annual Report on Form 10-K. The Form 10-K is
available upon request from the Corporate Trustee.

SPECIAL COST ESCROW ACCOUNT

     The Conveyance provides for reserving funds for estimated future "Special
Costs" of plugging and abandoning wells, dismantling platforms and other costs
of abandoning the Royalty Properties, as well as for the estimated amount of
future drilling projects and other capital expenditures on the Royalty
Properties. As provided in the Conveyance, the amount of funds to be reserved is
determined based on factors including estimates of aggregate future production
costs, aggregate future Special Costs, aggregate future net revenues and actual
current net proceeds. Deposits into this account reduce current distributions
and are placed in an escrow account and invested in short-term certificates of
deposit. Such account is herein referred to as the "Special Cost Escrow
Account." The Trust's share of interest generated from the Special Cost Escrow
Account serves to reduce the Trust's share of allocated production costs.
Special Cost Escrow funds will generally be utilized to pay Special Costs to the
extent there are not adequate current net

                                       11
<PAGE>
proceeds to pay such costs. Special Costs that have been paid are no longer
included in the Special Cost Escrow calculation. Deposits to the Special Cost
Escrow Account will generally be made when the balance in the Special Cost
Escrow Account is less than 125% of future Special Costs and there is a Net
Revenues Shortfall (a calculation of the excess of estimated future costs over
estimated future net revenues pursuant to a formula contained in the
Conveyance). When there is not a Net Revenues Shortfall, amounts in the Special
Cost Escrow Account will generally be released, to the extent that Special Costs
have been incurred. Amounts in the Special Cost Escrow Account generally will
also be released when the balance in such account exceeds 125% of future Special
Costs. In the first quarter of 1998, there was a net release of funds from the
Special Cost Escrow Account. The Trust's share of the funds released was
approximately $513,800. The release was primarily a result of a decrease in the
current estimates of projected capital expenditures, production costs and
abandonment costs of the Royalty Properties. In the first quarter of 1999, there
was a deposit of funds into the Special Cost Escrow Account. The Trust's share
of the funds deposited was approximately $461,000. The deposit was primarily a
result of an increase in the current estimate of projected capital expenditures
of the Royalty Properties. As of March 31, 1999, approximately $3,790,000
remained in the Special Cost Escrow Account.

     Chevron, in its capacity as Managing General Partner, has advised the Trust
that additional deposits to the Special Cost Escrow Account may be required in
future periods in connection with other production costs, other abandonment
costs, other capital expenditures and changes in the estimates and factors
described above. Such deposits, if made, could result in a significant reduction
in Royalty income in the periods in which such deposits are made, including the
possibility that no Royalty income would be received in such periods.

                                       12
<PAGE>
OVERVIEW OF PRODUCTION, PRICES AND NET PROCEEDS

     The following schedule provides a summary of the volumes and weighted
average prices for crude oil and condensate and natural gas recorded by the
Working Interest Owners for the Royalty Properties, as well as the Working
Interest Owners' calculations of the net proceeds and the royalties paid to the
Trust during the periods indicated. Net proceeds due to the Trust are calculated
for each three month period commencing on the first day of February, May, August
and November.

<TABLE>
<CAPTION>
                                                ROYALTY PROPERTIES
                                                THREE MONTHS ENDED
                                                   MARCH 31,(1)
                                          ------------------------------
                                             1999(3)           1998
                                          --------------  --------------
<S>                                       <C>             <C>
Crude oil and condensate (bbls).........         254,171         342,275
Natural gas and gas products (Mcf)......        (567,960)      1,355,007
Crude oil and condensate average price,
  per bbl...............................  $        10.09  $        17.24
Natural gas average price, per Mcf
  (excluding gas products)..............  $         2.11  $         2.75
Crude oil and condensate revenues.......  $    2,564,158  $    5,902,006
Natural gas and gas products revenues...      (1,245,133)      3,670,052
Production expenses.....................        (937,221)       (597,180)
Capital expenditures....................        (853,236)     (3,161,966)
Undistributed Net Loss (Income)(2)......       2,670,179        (129,859)
(Provision for) Refund of escrowed
  special costs.........................      (1,843,927)      2,055,287
                                          --------------  --------------
NET PROCEEDS............................         354,820       7,738,340
Royalty interest........................            x25%            x25%
                                          --------------  --------------
Partnership share.......................          88,705       1,934,585
Trust interest..........................         x99.99%         x99.99%
                                          --------------  --------------
Trust share.............................  $       88,696  $    1,934,392
                                          ==============  ==============
</TABLE>

------------

(1) The amounts for the three months ended March 31, 1999 and 1998 represent
    actual production for the periods November 1998 through January 1999, and
    November 1997 through January 1998, respectively.

(2) Undistributed net loss represents negative Net Proceeds generated during the
    respective period. An undistributed net loss is carried forward and offset,
    in future periods, by positive Net Proceeds earned by the related Working
    Interest Owner(s). Undistributed net income represents positive Net
    Proceeds, generated during the respective period, that were applied to an
    existing loss carryforward. As of March 31, 1999, the loss carryforward was
    $4,179,060 ($1,044,765 net to the Trust).

(3) During the first quarter of 1999, the Working Interest Owner of East Cameron
    371/381 informed the Trust that the Working Interest Owner overpaid East
    Cameron 371/381 royalties, related primarily to natural gas production, to
    the Trust in the third and fourth quarters of 1998. The total gas revenue
    and volume reported to the Trust was $5,696,741 ($1,424,185 net to the
    Trust) and 2,761,549 Mcf (690,387 Mcf net to the Trust), respectively. The
    amount that should have been reported to the Trust for gas revenue and
    volume was $1,424,185 ($356,046 net to the Trust) and 690,387 Mcf (172,597
    Mcf net to the Trust), respectively. As a result of these miscalculations
    and other minor adjustments, the Working Interest Owner overpaid the Trust
    royalties totaling $1,090,367. The Working Interest Owner of East Cameron
    371/381 recouped $404,190 of the overpayment from production in the first
    quarter of 1999 and will recoup additional royalties of $686,177 in future
    periods through future production on this property and West Cameron 643,
    which properties are operated by this Working Interest Owner.

                                       13

<PAGE>
                          PART II -- OTHER INFORMATION

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.

(A)  EXHIBITS

     (Asterisk indicates exhibit previously filed with the Securities and
Exchange Commission and incorporated herein by reference.)

<TABLE>
<CAPTION>
                                                                                  SEC FILE OR
                                                                                 REGISTRATION      EXHIBIT
                                                                                    NUMBER         NUMBER
                                                                                 -------------     -------
<S>           <C>                                                                <C>               <C>
4(a)*     --  Trust Agreement dated as of January 1, 1983, among Tenneco
              Offshore Company, Inc., Texas Commerce Bank National
              Association, as corporate trustee, and Horace C. Bailey, Joseph
              C. Broadus and F. Arnold Daum, as individual trustees (Exhibit
              4(a) to Form 10-K for the year ended December 31, 1992 of TEL
              Offshore Trust)................................................        0-6910           4(a)
4(b)*     --  Agreement of General Partnership of TEL Offshore Trust
              Partnership between Tenneco Oil Company and the TEL Offshore
              Trust, dated January 1, 1983 (Exhibit 4(b) to Form 10-K for
              year ended December 31, 1992 of TEL Offshore Trust)............        0-6910           4(b)
4(c)*     --  Conveyance of Overriding Royalty Interests from Exploration I
              to the Partnership (Exhibit 4(c) to Form 10-K for year ended
              December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(c)
4(d)*     --  Amendments to TEL Offshore Trust Trust Agreement, dated
              December 7, 1984 (Exhibit 4(d) to Form 10-K for year ended
              December 31, 1992 of TEL Offshore Trust).......................        0-6910           4(d)
4(e)*     --  Amendment to the Agreement of General Partnership of TEL
              Offshore Trust Partnership, effective as of January 1, 1983
              (Exhibit 4(e) to Form 10-K for year ended December 31, 1992 of
              TEL Offshore Trust)............................................        0-6910           4(e)
10(a)*    --  Purchase Agreement, dated as of December 7, 1984 by and between
              Tenneco Oil Company and Tenneco Offshore II Company (Exhibit
              10(a) to Form 10-K for year ended December 31, 1992, of TEL
              Offshore Trust)................................................        0-6910          10(a)
10(b)*    --  Consent Agreement, dated November 16, 1988, between TEL
              Offshore Trust and Tenneco Oil Company (Exhibit 10(b) to Form
              10-K for year ended December 31, 1988 of TEL Offshore Trust)...        0-6910          10(b)
10(c)*    --  Assignment and Assumption Agreement, dated November 17, 1988,
              between Tenneco Oil Company and TOC-Gulf of Mexico Inc.
              (Exhibit 10(c) to Form 10-K for year ended December 31, 1988 of
              TEL Offshore Trust)............................................        0-6910          10(c)
10(d)*    --  Gas Purchase and Sales Agreement Effective September 1, 1993
              between Tennessee Gas Pipeline Company and Chevron U.S.A.
              Production Company (Exhibit 10(d) to Form 10-K for year ended
              December 31, 1993 of TEL Offshore Trust).......................        0-6910          10(d)
27(a)     --  Financial Data Schedule
</TABLE>

(B)  REPORTS ON FORM 8-K

     No reports on Form 8-K were filed with the Securities and Exchange
Commission during the first quarter of 1999.

                                       14
<PAGE>
                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.

                                          TEL OFFSHORE TRUST
                                          By:  Chase Bank of Texas, National
                                               Association, Corporate Trustee
                                          By:  /s/    PETE FOSTER
                                                      PETE FOSTER
                                                  SENIOR VICE PRESIDENT
                                                    AND TRUST OFFICER

Date: May 10, 1999

The Registrant, TEL Offshore Trust, has no principal executive officer,
principal financial officer, board of directors or persons performing similar
functions. Accordingly, no additional signatures are available and none have
been provided.

                                       15